Real-Time Adaptive Cruise Control under Sensor Uncertainty using Interval Type-2 Fuzzy Logic on a Low-Cost Experimental Vehicle Platform

2.1 Methodology and implementation

In this study, an ACC system was developed for an experimental vehicle and tested on a straight track. The system was designed to maintain the vehicle’s speed while automatically adjusting the safe distance to the object ahead. The controller was implemented using an IT2FLS, which processes inputs in the form of the distance to the vehicle ahead and the vehicle’s speed to generate a control signal in the form of PWM modulation. The entire data processing and control signal transmission process is performed in real-time via an ESP32 microcontroller connected to the system’s sensors and actuators.

2.2 Adaptive Cruise Control

ACC is a system or concept in the automotive industry, primarily used in cars, that maintains the vehicle’s speed at a level set by the driver. When there is a vehicle ahead traveling at a slower speed, this system adjusts the vehicle’s speed to match that of the vehicle in front [17, 18]. The following describes the operating principle of ACC, as shown in Figure 1.

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Figure 1. How Adaptive Cruise Control (ACC) works [19]

The development of the ACC system is designed to reduce the burden on drivers who need to control the accelerator and brake pedals while steering the vehicle over long periods of time. The system uses data such as the distance ahead of the vehicle and the vehicle’s speed, as well as several additional sensors, to make decisions [20, 21]. The mathematical calculations in this system use standard methods, such as calculating the safe distance between vehicles, as shown in Eq. (1). To calculate the estimated time and distance between vehicles, Eqs. (2) and (3), and several other equations are used.

${{d}_{safe}}={{t}_{h}}{{v}_{f}}+{{d}_{0}}$      (1)

${{t}_{h}}={{t}_{0}}-{{c}_{v}}{{v}_{ref}}$      (2)

${{t}_{h}}={{t}_{0}}-{{c}_{v}}{{v}_{ref}}-{{c}_{a}}{{a}_{p}}$         (3)

2.3 Interval Type 2 Fuzzy Logic System

The IT2FLS is an extension of the Type-1 Fuzzy Logic System (T1FLS) designed to handle uncertainty in nonlinear and dynamic systems. In ACC systems, uncertainty arises due to sensor noise, variations in environmental conditions, and vehicle dynamics [22, 23]. Therefore, IT2FLS is used to improve the robustness of the control system. Unlike T1FLS, which assigns only one membership degree to each input value, IT2FLS represents the input using an interval of membership values. This interval-based representation enables the controller to tolerate fluctuations in sensor readings, such as distance variation from the IR sensor and acceleration noise from the MPU6050 sensor.

1. Membership function

In an IT2FLS denoted by $\tilde{A},$ which has the membership function ${{\mu }_{{\tilde{A}}}}\left( x,u \right)$, where $x\in X~$and $u\in {{j}_{x}}\subseteq \left[ 0,1 \right]$ the type-2 fuzzy set can be written as shown in Eq. (4). Where if $0\le {{\mu }_{{\tilde{A}}}}\left( x,u \right)\le 1$, $\tilde{A}$ can be written as shown Eq. (5).

$\tilde{A}=\{\left( \left( x,u \right),{{\mu }_{{\tilde{A}}}}\left( x,u \right) \right)~|~\forall ~x\in X~~\forall ~u\in {{j}_{x}}\subseteq \left[ 0,1 \right]\}$         (4)

$\tilde{A}=\mathop{\int }_{x\epsilon X}^{~}\mathop{\int }_{u\epsilon {{j}_{x}}}^{~}\frac{{{\mu }_{{\tilde{A}}}}\left( x,u \right)}{\left( x,u \right)}~{{j}_{x}}\subseteq \left[ 0,1 \right]$       (5)

For every value of x = x’, in a two-dimensional plane where the axes are u and ${{\mu }_{{\tilde{A}}}}\left( x',u \right)$, the vertical slice is called the secondary membership function. A secondary membership function, which is a vertical section ${{\mu }_{{\tilde{A}}}}\left( x,u \right)$ is ${{\mu }_{{\tilde{A}}}}\left( x=x',u \right)$ for ${x}'\epsilon X$ and $\forall u~\epsilon {{j}_{{{x}'}}}~\subseteq \left[ 0,1 \right]$ can be written as shown in the Eq. (6).

${{\mu }_{{\tilde{A}}}}\left( x={x}',u \right)={{\mu }_{{\tilde{A}}}}\left( {{x}'} \right)=\mathop{\int }_{u\in {{j}_{x'}}}^{~}\frac{{{f}_{{{x}'}}}\left( u \right)}{\left( u \right)}~{{j}_{x'}}\subseteq \left[ 0,1 \right]$       (6)

The following is the IT2FLS membership function shown in Figure 2.

A secondary membership function interval reflects a uniform uncertainty in the primary membership of x. This is because all memberships in a type-1 set are unitary; consequently, a type-1 set is represented only by the domain of the interval, which is defined by the left and right endpoints [24]. In this study, the interval is used to represent uncertainty in the ACC input variables. For example, when the IR sensor reads a distance value, the actual value may fluctuate because of vibration, surface irregularity, or electrical interference. Therefore, IT2FLS does not process the sensor value as a single crisp membership degree, but as a bounded uncertainty region. The following is the IT2FLS block diagram shown in Figure 3.

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Figure 2. Membership features Interval Type-2 Fuzzy Logic System (IT2FLS)

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Figure 3. Diagram block Interval Type-2 Fuzzy Logic System (IT2FLS)

These two endpoints are associated with two types of membership functions, represented as the upper and lower membership functions, which are bounded by the footprint of uncertainties (FOU). The upper membership function (UMF) is associated with the boundary at the top of the FOU (Ã) and is denoted by ${{\bar{\mu }}_{{\tilde{A}}}}\left( x \right),\forall x\in X$. Where the Lower membership function (LMF) is associated with the bottom boundary of the FOU ($\tilde{A})$ and is represented by ${{\underset{\scriptscriptstyle-}{\mu }}_{{\tilde{A}}}}\left( x \right),\forall x\in X$. The area between the UMF and LMF is called the Footprint of Uncertainty. In the proposed ACC system, the FOU provides a tolerance region for uncertain sensor inputs before the control decision is converted into PWM modulation. This mechanism is expected to reduce abrupt PWM changes caused by sudden sensor fluctuations.

2. Fuzzy function

This IT2FLS control system uses shoulder curves and triangular curves. It has two inputs: data from the IR sensor and the MPU6050 sensor, which have linguistic values (UMF and LMF). The IR sensor and the MPU6050 sensor have different membership functions because the vehicle’s distance and speed vary [15]. The Fuzzy Inference System (FIS) model used is the Multiple-Input Single-Output (MISO) model, which uses readings from the IR sensor and the MPU6050 sensor as inputs. These inputs are processed using a rule editor, which then generates an output in the form of a PWM adjustment (defuzzification), as shown in Figure 4. In this stage, the distance input represents the spacing between the experimental vehicle and the object ahead, while the speed input represents the vehicle motion condition derived from the inertial sensor. Both inputs are fuzzified into linguistic variables using UMF and LMF to preserve uncertainty information before entering the inference stage.

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Figure 4. Model FIS Multiple-Input Single-Output (MISO)

The following are the membership sets of the variables IT2FLS, speed, and distance, which are the system inputs, namely:

1. IT2FS speed variable

The velocity membership function (ve) is an input signal consisting of five sets: “Very Slow (SL)” (≤21 cm/s & ≤19 cm/s), “Slow (L)” (9–31 cm/s & 11–29 cm/s), “Normal (N)” (19–41 cm/s and 21–39 cm/s), “Fast (C)” (29–51 cm/s and 31–49 cm/s), and “Very Fast (SC)” (≥39 cm/s and ≥41 cm/s). The following are the membership degrees of the IT2FLS velocity variable, which consists of 5 sets, as shown in Figure 5. The use of two boundary values in each linguistic set indicates that the speed input is not treated as a fixed value, but as an uncertain interval. This is important because acceleration and velocity estimation from the MPU6050 may be affected by vibration and sensor drift.

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Figure 5. Degree of freedom of the velocity variable

2. IT2FLS distance variable

The distance membership function (d) is an input signal consisting of five sets: “Very Close (SD)” (≤ 38 cm & ≤ 42 cm), “Close (D)” (18–62 cm & 22–58 cm), “Normal (N)” (38–82 cm & 42–78 cm), “Far (F)” (58–102 cm & 62–98 cm), and “Very Safe (VS)” (≤ 78 cm & ≤ 82 cm). Figure 6 shows the membership degrees of the distance variable IT2FLS, which consists of 5 sets, as shown in Figure 6. The interval distance membership function enables the controller to handle uncertainty in the IR sensor reading. Thus, when the measured distance fluctuates near the boundary between two linguistic categories, the IT2FLS can still produce a gradual control response instead of an abrupt decision.

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Figure 6. Degree of membership of the distance variable

3. IT2FLS Variable PWM Change

The PWM (defuzzy) control uses membership degrees divided into four categories: “high acceleration (PCB)” (20), “acceleration (PC)” (10), “deceleration (PB)” (-10), and “high deceleration (PBB)” (-20). The PWM change is used as the control output to regulate motor speed. Positive values increase the PWM signal for acceleration, whereas negative values reduce the PWM signal for deceleration. Therefore, the fuzzy output directly determines how the vehicle responds to distance and speed variations.

3. Inference

After performing fuzzification by defining membership functions, a rule base was constructed using the basic rule IF x is A AND IF y is B THEN z is C, which is divided into upper and lower sets. The following is the rule base of the IT2FL system, as shown in Table 1. The rule base connects the distance and speed conditions with the required PWM adjustment. For example, when the vehicle is too close to the object ahead and its speed is high, the controller produces a deceleration output. Conversely, when the distance is safe and the vehicle speed is low, the controller can generate an acceleration output. This rule mechanism links the IT2FLS architecture directly to the ACC objective, namely maintaining a safe distance and stable speed.

Table 1. Table of rule base

The following are the variable descriptions from Table 1:

SL: Membership degree “Very Slow”

L: Membership degree “Slow”

S: Membership degree “Standard”

C: Membership degree “Fast”

S: Membership degree “Very Fast”

SJ: Membership degree “Very Far”

D: Membership degree “Far”

N: Membership degree “Normal”

D: Membership degree “Near”

SD: Membership degree “Very Near”

PCB: Membership degree “High Acceleration”

PC: Membership degree “Acceleration”

PB: Membership degree “Deceleration”

PBB: Membership degree “High Deceleration”

To avoid ambiguity in the rule notation, the distance linguistic labels should be consistently written as Very Far, Far, Normal, Near, and Very Near, while the speed linguistic labels should be written as Very Slow, Slow, Standard, Fast, and Very Fast. This consistency helps clarify the relationship between input conditions and PWM output decisions.

4. Type-reducer

Type reduction is a process step for reducing the IT2FLS set to a Type 1 fuzzy set. In this process, the reduction method used is the center-of-set method, as described in Eqs. (7) and (8) [25]. The type-reduction stage combines the firing strengths obtained from the UMF and LMF to produce an output interval. This interval represents the possible range of control actions under uncertain input conditions.

$y\left( {{\theta }_{1}},\ldots ,~{{\theta }_{Z}} \right)=\frac{\mathop{\sum }_{z=1}^{Z}{{y}_{z}}{{\theta }_{z}}}{\mathop{\sum }_{z=1}^{Z}{{\theta }_{z}}}$        (7)

${{y}_{lk}}=\frac{\mathop{\sum }_{i=1}^{M}f_{l}^{i}y_{lk}^{i}}{\mathop{\sum }_{i=1}^{M}f_{l}^{i}}$        (8)

5. Defuzzification

In the type-reduction stage, the output of each type-reduced set is determined by the leftmost point ${{y}_{lk}}$and the rightmost point ${{y}_{rk}}$. The set interval is defuzzified using the average of ${{y}_{lk}}$ and ${{y}_{rk}}$; therefore, the defuzzified crisp output for each output k can be written as in Eq. (9).

${{y}_{k}}\left( x \right)=\frac{{{y}_{lk}}+{{y}_{rk}}}{2}$       (9)

In the developed system, IT2FLS receives two main inputs: the distance between the vehicle and the object ahead (d) and the vehicle’s speed (v). The output, which is the change in PWM (ΔPWM), is used to control the vehicle’s acceleration or deceleration [26]. The final crisp output is then sent to the ESP32 as a PWM adjustment command for the motor driver. Consequently, the complete IT2FLS process can be summarized as follows: uncertain distance and speed inputs are fuzzified using UMF and LMF, processed through the rule base, reduced into an output interval, defuzzified into a crisp ΔPWM value, and applied to regulate vehicle motion in real time. This sequence explains how the IT2FLS block contributes to smoother PWM modulation and more adaptive ACC behavior in the experimental results.

2.4 Ackermann steering

When turning a vehicle, if the centers of all the wheels coincide at a single point, the vehicle will turn around that point, resulting in pure rolling motion. This condition is known as the Ackermann condition, and this principle is known as the Ackermann principle. Figure 7 illustrates the kinematics of Ackermann steering.

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Figure 7. Ackermann steering kinematics [27]

Ackermann steering geometry is most commonly used in commercial vehicles. The purpose of Ackermann steering is to prevent the tires from sliding sideways when following a curved road and to improve maneuverability at low speeds [28]. The following are the equations used in Ackermann steering kinematics:

1. The Ackermann angle in Eq. (10).

$\propto =ta{{n}^{-1}}\left( \frac{\frac{c}{2}}{b} \right)$      (10)

2. Inner wheel lock-up angle in Eq. (11).

$sin\theta =b-\frac{a-c}{2}$      (11)

3. The locking angle of the outer wheel in Eq. (12).

​$cot\varphi -cot\theta =\frac{c}{b}$     (12)

4. Inner front wheel turning radius in Eq. (13).

${{T}_{IF}}=\frac{b}{sin\theta }-\frac{a-c}{2}$     (13)

5. The turning radius of the outer front wheel in Eq. (14).

${{T}_{OF}}=\frac{b}{sin\theta }-\frac{a-c}{2}$     (14)

6. The average turning radius in Eq. (15).

${{T}_{R}}=\frac{{{T}_{IF}}-{{T}_{OF}}}{2}$          (15)

7. The value of Ackermann in Eq. (16).

$nilai~ackermann=ta{{n}^{-1}}\left( \frac{b}{\frac{b}{tan\theta }-a} \right)$        (16)

8. Ackermann % in Eq. (17).

$ackerman\%=\frac{\theta}{\text { value of ackermann }} \times 100$        (17)

where,

$a$ = wheel track, or the distance between the left and right wheels

b = wheelbase or the distance between the front and rear wheels

c = distance between pivot

$\theta $ = inner wheel lock angle

$\varphi $ = outer wheel lock angle

${{T}_{IF}}$ = inner front wheel turning radius

${{T}_{OF}}$ = outer front wheel turning radius

${{T}_{R}}\text{ }\!\!~\!\!\text{ }$= average turning radius

In the ACC system, Ackermann steering kinematics are applied in the design of the vehicle's steering kinematics to make the vehicle's steering system as similar as possible to that of a real car and to ensure good stability while the vehicle is in motion.

2.5 Device design

The experimental vehicle system adopts Ackermann steering kinematics, with the two rear wheels as the drive wheels and the two front wheels controlled by a servo motor. Rear drive motors are mounted to maintain center-of-gravity balance and stable propulsion.

The vehicle has a two-layer structure: the first layer houses mechanical components and the IR sensor, while the second layer houses electronic components such as the ESP32, MPU6050, and servo motor. The acrylic frame (3 mm thick, 400 × 200 mm) provides structural support and stability for the steering system.

Figure 8 shows the mechanical layer (Layer 1) with key components:

1. Steering system – vehicle direction control
2. IR sensor – measures distance to obstacles
3. Battery 1 – powers the control circuitry
4. Motor driver – receives PWM from IT2FLS to control DC motors
5. Battery 2 – powers the drive motors
6. Rear drive wheels – vehicle propulsion
7. DC motors – drive the rear wheels

Figure 9 shows the electronic layer (Layer 2) with:

8. Servo – controls front-wheel steering
9. ESP32 – executes IT2FLS processing in real time
10. MPU6050 – provides vehicle speed and acceleration feedback

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Figure 8. Design system vehicle layer 1

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Figure 9. Design system vehicle layer 2

Functional Integration with IT2FLS:

1. The IR sensor and MPU6050 provide inputs representing the vehicle’s distance to obstacles and its speed.
2. Sensor data are pre-processed (filtered and normalized) in the Sensor Data Processing module (Section 2.4).
3. Processed data are input into the IT2FLS module on the ESP32, which calculates the required PWM adjustment.
4. PWM outputs are sent to the motor driver to adjust vehicle speed, while the servo motor handles steering adjustments.

This design emphasizes functional integration rather than detailed mechanical layout, showing how each component contributes to real-time IT2FLS-based ACC performance.

2.6 Electronic circuit

To achieve good movement and control of the vehicle, a properly designed electronic circuit is required. This electronic circuit is designed to process sensor readings, control the drive motors, and control the steering servo motor. The following is the electronic circuit for the vehicle shown in Figure 10.

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Figure 10. Electronic circuit

2.7 Block diagram system

The system block diagram illustrates the workflow of each component in the vehicle as a closed-loop control system, ensuring that the process operates in a repetitive and continuous manner. As shown in Figure 11, the system begins by measuring the distance to the vehicle ahead and the ego vehicle’s speed; this data is then processed in the fuzzy logic block to determine the required speed limits and deceleration. Next, the IT2FLS output is processed by the microcontroller into a control signal that is transmitted to the motor driver to drive the motor.

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Figure 11. Adaptive Cruise Control (ACC) block diagram for the vehicle

Figure 11 identifies several variables that influence the process; the following is an explanation of those variables:

1. V1: host motor speed setpoint variable ($cm/s$)
2. ve: motor speed error variable ($cm/s$)
3. vst: motor speed after processing variable
4. sd: safe distance variable in this study is 50 cm
5. d: distance variable between the ego vehicle and the lead vehicle (cm)
6. Δd: vehicle distance relative to the safe distance: d - sd (cm)
7. defuzzy: PWM adjustment variable

2.8 Flowchart system

Figure 12 shows the flowchart of the main vehicle system. First, the input values from the IR sensor and MPU6050 are read. Then, the system checks whether the driver has pressed the switch to activate the system. If the switch is activated, the Adaptive Cruise Control System (ACCS) will engage, and the functions of the accelerator and brake pedals will correspond to the switch settings. To deactivate the system and return to manual drive mode, the driver must press the switch. If the switch is turned off, the system immediately enters manual drive mode. In the ACCS sub-process flowchart, the system begins by reading the vehicle’s speed and distance variables, followed by the IT2FLS method sub-flowchart and the ACC sub-flowchart, as shown in Figure 13.

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Figure 12. Main flowchart system

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Figure 13. Sub-flowchart Adaptive Cruise Control System (ACCS)

In the IT2FLS method sub-flowchart, the process begins by reading inputs from the IR sensor and the MPU6050 sensor, then proceeds through several steps as shown in Figure 14, resulting in an output variable representing the (defuzzied) PWM change.

Sub-flowchart The IT2FLS method sub-flowchart generates the required (defuzzified) PWM change output variable. This defuzzified variable serves as an input to the ACC sub-flowchart. It then becomes one of the inputs in the ACC sub-flowchart, as shown in Figure 15.

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Figure 14. Sub-flowchart Interval Type-2 Fuzzy Logic System (IT2FLS)

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Figure 15. Sub-flowchart Adaptive Cruise Control (ACC)

Figures 12 through 15 identify several variables that influence the process; the following is an explanation of those variables:

1. vs0: initial setpoint speed variable ($cm/s$)
2. vst: current setpoint speed variable ($cm/s$)
3. v1: host vehicle speed variable ($cm/s$)
4. d: distance between the host vehicle and the lead vehicle (cm)
5. ds: safe distance variable (cm)
6. Δd: vehicle distance minus safe distance: d - ds (cm)
7. j: PWM variable
8. defuzzy: PWM change variable ($cm/{{s}^{2}}$)

This study demonstrates that the application of the IT2FLS in an ACC system is capable of improving control performance compared to manual testing. On a 6-meter track, the IT2FLS-based system achieved an average travel time of 34 seconds, which is shorter than the 44.6 seconds recorded in manual testing. In terms of sensor readings, the IT2FLS method also provided better results, with a distance reading success rate of 89.061% and an acceleration success rate of 88.135%, whereas manual testing only achieved 87.934% for distance readings and 81.664% for acceleration. Additionally, the average PWM change in the IT2FLS system was 8.559, which is smaller than the 10 recorded in the manual test, indicating that the system is capable of producing a smoother and more adaptive control response. These results confirm that the IT2FLS block effectively converts uncertain sensor inputs into stable PWM outputs, providing adaptive real-time control that maintains vehicle speed and safe distance.

Nevertheless, the system’s performance is still influenced by the quality of sensor readings. Disturbances such as noise caused by track irregularities and electromagnetic interference from other components can result in PWM outputs that do not always match the expected values. Moreover, the experiments were limited to straight tracks, so performance under curved paths or dynamic acceleration/deceleration scenarios was not evaluated.

For future research, the system can be further developed by integrating more stable sensors, enhancing data communication reliability, implementing braking mechanisms, and testing on more complex track conditions including curves and uneven terrain. These improvements will allow IT2FLS-based ACC to be validated under realistic dynamic driving scenarios.